The political dividing lines were not as clear as they are for modern day political parties, but the two groups differed on several key issues. The Girondists supported foreign wars and a federalist government in the style of the newly-formed United States. The Montagnards on the other hand, opposed the wars and believed that Paris should predominate in politics.

The Girondists initially held most of the political power, but a series of political defeats led to their fall from grace and the rise of the Montagnards.
By this time, Robespierre had grown obsessed with conspiracies, especially among his political opponents. On June 1 and 2, members of the Girondists were placed under house arrest*, and moved to prison several weeks later. In October, 1793, 23 of the Girondists were executed for treason**.
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* Which makes it sound tidy - in reality Hanriot drove cannons up to the National Convention and threatened to fire if the politicians didn't give up the Girondists.
** ACTIVATE SARCASM. And received a totally fair trial too, I'm sure. END SARCASM.